Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition

TL;DR

This paper investigates how boundary conditions affect the universal statistics of topological defects generated during phase transitions, revealing that boundary effects become significant in slow quenches, breaking the expected power-law scaling.

Contribution

It demonstrates that boundary conditions influence the defect number distribution's cumulants, especially in slow quenches, extending understanding beyond the standard Kibble-Zurek mechanism.

Findings

Cumulants follow universal power-law scaling for fast/moderate quenches regardless of boundary conditions.

In slow quenches, boundary conditions cause deviations from the universal power-law behavior.

Theoretical predictions are validated with a one-dimensional scalar lattice model.

Abstract

In a scenario of spontaneous symmetry breaking in finite time, topological defects are generated at a density that scale with the driving time according to the Kibble-Zurek mechanism (KZM). Signatures of universality beyond the KZM have recently been unveiled: The number distribution of topological defects has been shown to follow a binomial distribution, in which all cumulants inherit the universal power-law scaling with the quench rate, with cumulant rations being constant. In this work, we analyze the role of boundary conditions in the statistics of topological defects. In particular, we consider a lattice system with nearest-neighbor interactions subject to soft anti-periodic, open, and periodic boundary conditions implemented by an energy penalty term. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate that is independent of the boundary conditions except by an additive term, that becomes prominent in the limit of slow quenches, leading to the breaking of power-law behavior. We test our theoretical predictions with a one-dimensional scalar theory on a lattice.